SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence

TL;DR

This paper introduces a new model for the dS/CFT correspondence using a Yang-Baxter operator for the deSitter group, leading to dual conformal quantum field theories in deSitter spacetime and Euclidean space.

Contribution

It constructs a Yang-Baxter operator satisfying key properties and uses it to develop dual conformal field theories related to deSitter space and its boundary.

Findings

Defined a Yang-Baxter operator for SO(d,1)

Constructed a chiral conformal QFT in deSitter space

Established duality with Euclidean conformal QFT

Abstract

We propose a model for the dS/CFT correspondence. The model is constructed in terms of a "Yang-Baxter operator" $R$ for unitary representations of the deSitter group $SO(d,1)$. This $R$-operator is shown to satisfy the Yang-Baxter equation, unitarity, as well as certain analyticity relations, including in particular a crossing symmetry. With the aid of this operator we construct: a) A chiral (light-ray) conformal quantum field theory whose internal degrees of freedom transform under the given unitary representation of $SO(d,1)$. By analogy with the $O(N)$ non-linear sigma model, this chiral CFT can be viewed as propagating in a deSitter spacetime. b) A (non-unitary) Euclidean conformal quantum field theory on ${\mathbb R}^{d-1}$, where $SO(d,1)$ now acts by conformal transformations in (Euclidean) spacetime. These two theories can be viewed as dual to each other if we interpret ${\mathbb R}^{d-1}$ as conformal infinity of deSitter spacetime. Our constructions use semi-local generator fields defined in terms of $R$ and abstract methods from operator algebras.